How much must be invested today at 10 %, compounded continuously, to be worth $165,000 in 5 years? Pick the closest answer. [Use e = 2.71]
Question
How much must be invested today at 10 %, compounded continuously, to be worth $165,000 in 5 years?
Pick the closest answer.
[Use e = 2.71]
Solution
To solve this problem, we will use the formula for continuous compounding, which is:
A = P * e^(rt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (decimal) t = time the money is invested for in years
We know that A = $165,000, r = 10% or 0.10, t = 5 years, and we need to find P.
Rearranging the formula to solve for P gives us:
P = A / e^(rt)
Substituting the given values into the formula gives us:
P = 165000 / 2.71^(0.10*5)
Now, calculate the value of P.
P = 165000 / 2.71^(0.5)
P = 165000 / 1.6487212707
P = $100,000.17
So, approximately 165,000 in 5 years.
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